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Inexact non-interior continuation method for monotone semidefinite complementarity problems

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Abstract

Chen and Tseng (Math Program 95:431–474, 2003) extended non-interior continuation methods for solving linear and nonlinear complementarity problems to semidefinite complementarity problems (SDCP), in which a system of linear equations is exactly solved at each iteration. However, for problems of large size, solving the linear system of equations exactly can be very expensive. In this paper, we propose a version of one of the non-interior continuation methods for monotone SDCP presented by Chen and Tseng that incorporates inexactness into the linear system solves. Only one system of linear equations is inexactly solved at each iteration. The global convergence and local superlinear convergence properties of the method are given under mild conditions.

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Authors and Affiliations

  1. Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Shaoping Rui

  2. School of Mathematical Science, Huaibei Normal University, Huaibei, 235000, People’s Republic of China

    Shaoping Rui

  3. Hangzhou Institute of Service Engineering, Hangzhou Normal University, Hangzhou, 310012, People’s Republic of China

    Chengxian Xu

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  1. Shaoping Rui
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  2. Chengxian Xu
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Correspondence to Shaoping Rui.

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Rui, S., Xu, C. Inexact non-interior continuation method for monotone semidefinite complementarity problems. Optim Lett 6, 1411–1424 (2012). https://doi.org/10.1007/s11590-011-0337-8

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  • DOI: https://doi.org/10.1007/s11590-011-0337-8

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